相关论文: Generic Trace Semantics via Coinduction

We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…

We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with…

Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…

Spoiler-Duplicator games are used in finite model theory to examine the expressive power of logics. Their strategies have recently been reformulated as coKleisli maps of game comonads over relational structures, providing new results in…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

Eight categorical soundness and completeness theorems are established within the framework of algebraic theories. Exactly six of the eight deduction systems exhibit complete semantics within the cartesian monoidal category of sets. The…

Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…

Formal semantics offers a complete and rigorous definition of a language. It is important to define different semantic models for a language and different models serve different purposes. Building equivalence between different semantic…

We propose abstract compilation for precise static type analysis of object-oriented languages based on coinductive logic programming. Source code is translated to a logic program, then type-checking and inference problems amount to queries…

Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…

Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…

In this work, we study the notions of relative comonad and comodule over a relative comonad, and use these notions to give a terminal coalgebra semantics for the coinductive type families of streams and of infinite triangular matrices,…

For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\times Set$ and use the…

Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…

We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…

We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results…

We introduce continuation semantics for both fixpoint modal logic (FML) and Computation Tree Logic* (CTL*), parameterised by a choice of branching type and quantitative predicate lifting. Our main contribution is proving that they are…

Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…

Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to…

It is well-known that the category of Kleisli algebras for a monoidal monad carries a canonical monoidal structure. We define the notion of a commutative graded monad and present a strictly two-categorical proof that Kleisli algebras for…